stats final
p < .05 means that the difference between sample means
-fell outside the rejection region -should be attributed to chance rather than to the -- independent variable -should be declared "not significant" NONE OF THESE
independent samples t-test
Used to compare two means in a between-groups design (e.g., each participant is in only one condition)
A hypothesis was proposed, an alpha level of .05 adopted, data gathered, a mean computed, and a probability figure attached to the mean. Which of the probabilities below are in the rejection region?
.50
A one-factor repeated-measures ANOVA is designed for______________ independent variable(s).
1
Suppose you had on a single graph three chi square distributions with degrees of freedom of 1, 5 and 10. Choose a point on the X-axis and draw a vertical line. The distribution that would have the most area to the right of the vertical line would be the one with
10 df
Given the regression equation, Y = 5 + 0.5X, where X is a score on an attitude scale and Y is a job satisfaction score, what satisfaction score would be predicted for an attitude score of 20?
15
Suppose that college grade point average and the verbal portion of an IQ test had a correlation of .5. What percent of the variance do those two have in common?
25 percent
A research design had two independent variables: social class (upper, middle, working) and personality type (externalizer and internalizer). The dependent variable is a scale measuring locus of control. To analyze, one should use a
2x3 factorial ANOVA
A one-factor repeated-measures ANOVA partitions the total variance into _______ component(s).
3
In the regression equation: y = 30 + 1.5(x), if x was to increase by two units, how much change is expected in y?
3
Which alternative is most closely related to the concept of a two-tailed test of significance?
A divided rejection region
Treatment
A level/category of the independent variable/factor
Positive Correlation
Association between variables such that high scores on one variable tend to have high scores on the other variable
a priori
Based on reasoning, not immediate observation; planned tests
Sum of Squares, Error
Captures the sum of variability in each group
Sum of Squares, Total
Captures the total variability of the data
Sum of Squares, Treatment
Captures the variability of group means from the grand mean
Fail to reject the null hypothesis
Conclude that you did not find a statistically significant difference and Results do not support the research hypothesis
Reject the null hypothesis
Conclude that you found a statistically significant difference and Results are supportive of the research hypothesis
Which of the following can have a negative value?
DOES NOT have sum of squares, mean squares, F values.
In the same F test, it is possible to reject the null hypothesis at .01 but retain at .05.
False
Low F values go with low p values.
False
The Index f
Gives an overall effect size calculation for the study
Which of the following methods increases statistical power?
Increasing sample size
Which of the following statements describes a negative correlation?
More I eat the less I weigh.
degrees of freedom (df)
Refers to the number of scores that are free to vary when estimating a population parameter from a sample
The Pearson Correlation Coefficient
Sample correlation symbolized by r, Population correlation symbolized by ρ,Intended for scale data on both variables, Both a descriptive and inferential statistic, When used as NHST, the null is r = 0
Type I errors (α)
Sins of commission - rejecting the null hypothesis when it is true
Type II errors (β)
Sins of omission - failing to reject the null hypothesis when it is false
post hoc
Tests done after the F test; based on significance
Observed Frequencies
The actual distribution of your data
Expected Frequencies
The expected distribution of data if the two variables are unrelated; distribution if the null is true
Factor
The independent variable(s)
Odds Ratios
The most widely used statistic to express a relationship in a chi-square analysis is an odds ratio (odds: the chance that one thing will happen rather than another)
Suppose you calculated a correlation coefficient that was r = 0.12. What would be an appropriate interpretation?
There is a weak, positive correlation.
Paired-Samples Designs
Two samples with one independent variable
Chi-Square Tests of Independence
Used to test the association between two categorical variables Recall that the null hypothesis is that the two variables are independent of one another—thus, if we obtain a chi-square value greater than the critical value, we reject the null and argue that the two variables are related
The null hypothesis tested by the analysis of variance is that
all population means are the same
Researchers control the probability of a Type I error in their experiment by setting the value of
alpha
between-groups variance
an estimate of the population variance, based on the differences among the means
within-groups variance
an estimate of the population variance, based on the differences within each of the three (or more) sample distributions
Phi and the odds ratio
are effect size indexes
A repeated-measures ANOVA removes ________variance from further consideration.
between subjects
The F ratio in a repeated-measures ANOVA consists of the
between-treatments variance divided by the error variance
Theoretical frequencies in a test of independence are obtained
by assuming the categories of events are independent
Test of Independence:
calculated by multiplying the probability of each level in a variable and then multiplying it by the number of people in a sample
Goodness of Fit Test:
calculated by using proportions described in theory
To know the degrees of freedom for a chi square problem, you must know the number of
categories
In a goodness-of-fit test of a theory, the null hypothesis is that the data are
consistent with the theory
If you find that there is a logical reason to pair the scores from the two groups in a two-group experiment, you know whether
the design is a paired-samples or an independent-samples design
Which two phrases go with rejection of the null hypothesis?
dependence and poor theory
To find an odds ratio
divide the odds of event X by the odds of event Y
The null hypothesis for a test of independence is that the two variables are
independent
With an acknowledgment to Sesame Street, "Which of these things is not like the others, which of these things doesn't belong?"
independent samples
The Regression Equation
intercept - predicted value of Y when X is equal to 0 Slope - the amount that Y is predicted to increase for an increase of 1 in X
Suppose you have an experiment where you are comparing three groups. What would be the problem with conducting multiple t tests?
it will inflate the probability of a Type I Error
Variance is just another word for
mean square
The term main effect refers to a comparison of
means
RxC Notation:
notation of the factorial design in which the first number (R) refers to the number of levels in one IV while the second (C) refers to the number of levels in the second IV
From a factorial ANOVA with factors A and B, you can determine if
the differences among the A groups are significant the differences among the B groups are significant the interaction between the A variable and the B variable is significant
A cell in a factorial ANOVA refers to
one level of one independent variable and one level of a second independent variable
A student conducted a before and after study on college statistics students to see if the course improved ability to reason. In a later study, she used a mother-daughter sample to assess generational differences in attitudes toward abortion. Her two designs are
paired; paired
Suppose the cell means for a factorial ANOVA are presented as a line graph. Which of the following would indicate there was no significant interaction?
parallel lines
If an ANOVA with four samples produces a significant F, you can find out which samples are significantly different from the others by
performing HSD tests
Under which of the following conditions would you not use null hypothesis significance testing (NHST)?
population data are available
In statistics, a significant difference is one that is
probably not due to chance
critical value
refer to the threshold we use in making a decision about the null hypothesis
Suppose your data analysis produced an F value of 3.22. The appropriate F value in the table was only 3.20. You should
reject the null hypothesis and conduct post hoc testing
If the t test value is less than the critical value on the table, the null hypothesis even though you could be making a _____ error.
retain; Type II
Degrees of freedom are most closely related to
sample size
Null hypothesis significance testing (NHST) uses ______________ data to tell whether the ____________came from a(n)______________ population.
sample; sample; hypothesized
The 95 percent confidence interval about a mean difference was -3.0 minutes to 6.5 minutes. The null hypothesis that the two population means are equal
should be retained
Main Effect:
significance test of the deviations of the mean levels of one independent variable from the grand mean
The F distribution is
skewed
The terms "contingency table" or "cross-tab" go with
tests of independence only
The p in p < .05 is the probability
that the null hypothesis is true
Which of the following is (are) an assumption of ANOVA?
the form of the distribution of each population from which samples are drawn is normal, and the samples come from populations that have equal variances
In a simple experiment, treat two groups exactly the same except for one thing and then measure the individuals in both groups on some scale. Treating the two groups differently on the one thing constitutes
the independent variable
A one-factor repeated-measures ANOVA is like a paired-samples t test with respect to
the logical pairing of scores in a row
In simple linear regression, which point always falls on the line of best fit?
the mean X and mean of Y
Data were gathered, the results analyzed, and the null is rejected. Based on the logic of hypothesis testing, you can conclude that
the mean of the population from which the sample was drawn is probably not the mean specified by the null hypothesis
"There is no difference in the two populations" is a statement of
the null hypothesis
The value of K in an experiment depends on
the number of samples tested
The sum of the expected frequencies must be equal to
the sum of observed frequencies
If you have a paired-samples design, you can be sure that
there is a logical reason to pair the scores in the two groups
Interaction Effect:
when the effect of one independent variable on the dependent variable depends on the level of another independent variable
The t distribution, as a sampling distribution, gives the probability of events when
when the null hypothesis is true
If you have a regression equation
you can predict a score on one variable if you know a score on the other variable
The t distribution has a mean equal to
zero
